Flexibility trade‐offs in conservation offsets

Conservation offsets promise cost‐effective conservation of biodiversity, especially under economic and environmental change, because they represent a more flexible approach to biodiversity conservation, allowing for the economic development of ecologically valuable land provided that this development is offset by restoration of previously developed areas. The level of flexibility is determined by the trading rules. Lax rules allow for more flexibility, which promises cost savings, but will likely lead to unintended loss of biodiversity. I analyzed the trade‐off between economic costs and ecological benefits (biodiversity conservation) in biodiversity offsetting with an ecological‐economic model that considered the three main types of offset flexibility: spatial, temporal, and ecosystem type. I sought to examine the influence of ecological and economic conditions on offset flexibility trade‐offs. Large variation in the conservation costs and small costs of habitat restoration strongly increased trading activity and reduced the ecological benefit. The ecological benefit was most sensitive to spatial flexibility when a short range of ecological interaction was considered. At a large interaction range, spatial flexibility delivered large cost savings without overly reducing the ecological benefit. Risks and time lags associated with habitat restoration favored an offsetting scheme in which credits are awarded with the initiation of restoration projects rather than their successful completion—given appropriate offsetting multipliers were chosen. Altogether, under scarce resources, the level of flexibility in an offsetting scheme should be chosen by carefully balancing ecological benefits and economic costs.


INTRODUCTION
Conservation offsets are used worldwide and increasingly (Bull & Strange, 2018) to conserve biodiversity in the face of economic development.As such, they stand at the end of the mitigation and conservation hierarchy for dealing with adverse impacts of development on biodiversity-avoid, minimize, restore, offset (Milner-Gulland et al., 2021)-and should be considered only if these three policies are impossible or prohibitively costly.
Compared with the static protection of biodiversity, offsets provide a more dynamic and flexible approach to biodiversity conservation in which adverse impacts on biodiversity are not entirely forbidden but may be offset by adequate conservation (restoration) measures.Often this offsetting process is organized through a market in which restoration measures earn biodiversity credits that are sold to landowners who destroy biodiversity to develop their land for economic purposes.In an ideal market, the profit-oriented decisions of landowners imply that conservation and restoration measures are carried out at the least economically profitable sites, whereas development takes place at the most economically profitable sites.In theory, this promises a higher level of cost-effectiveness than static conservation schemes or planning approaches, so a given level of biodiversity can be conserved at a lower cost (Bull et al., 2015;Wissel & Wätzold, 2010).
However, flexibility implies that the biodiversity features lost and restored in the course of the offsetting process are often not identical ("out-kind" rather than "in-kind" [Bull et al., 2015]).In particular, the restored biodiversity feature may be structurally different from the lost one and may emerge at a different spatial location or at a later time due to the duration of the restoration project.There are three main types of biodiversity offsetting flexibility: spatial, temporal, and ecosystem type (Bull et al., 2015;Wissel & Wätzold, 2010;zu Ermgassen et al., 2020).
An additional problem is that restoration processes not only take time, but also may fail altogether, which inadvertently leads to biodiversity decline unless biodiversity credits are awarded only for complete and successful restoration projects (i.e., "savings banks") (Bekessy et al., 2010).This requirement, however, makes offsetting schemes unattractive to landowners, so in practice, many (or even most) schemes are "lending banks" (Bekessy et al., 2010) under which credits are earned at the initiation of a restoration project.To offset restoration failures, these lending banks usually include "multipliers" (Moilanen et al., 2009) so that, for example, 1 ha of lost ecologically valuable land can only be offset by the restoration of >1 ha of the same type of biodiversity.Such multipliers are used widely in practice (Bull et al., 2017).
Flexibility in conservation offsets creates advantages on the economic side and disadvantage on the ecological side such that the equivalence between lost and offset biodiversity is not guaranteed.Given there is often political pressure toward more flexibility, it is important to understand the circumstances under which flexibility is particularly critical and, because financial resources are often scarce, the circumstances under which a limited loss of biodiversity is associated with large cost savings.I built a simple ecological-economic model to systematically analyze the trade-off between cost savings and biodiversity loss associated with offsetting flexibility.
A few researchers have used models to analyze impacts of offsetting flexibility.Bull et al. (2015) distinguish among unaffected, lost, and gained biodiversity features in the course of offsetting dynamics and among ecosystem types.They explored impacts of flexibility in time and type by considering a number of offsetting scenarios.Flexibility in time led to different temporal changes in the levels of biodiversity, whereas flexibility in type could not guarantee all ecosystem types would be preserved.However, they considered only the ecological consequences of offsetting flexibility, disregarding the economic ones.Drechsler (2022) considered the ecological and economic dimensions and discussed whether conservation credits should be lending or savings banks and found that the most costeffective scheme type depends on the ecological and economic circumstances, such as the speed of economic change.
I took a similar approach, employing a much simpler model but allowing for consideration of all three types of flexibility.By simultaneously considering several dimensions of flexibility, I was able to explore interactions among these dimensions.Ecological and economic parameters characterizing the situation included spatial variation and correlation of conservation costs, restoration costs, the conservation agency's time preference, duration and success probability of restoration projects, and spatial ecological interaction range.I considered the levels of flexibility quasi-continuously in very small steps and varied our model parameters systematically to deliver a comprehensive understanding of the ecological and economic impacts of offsetting flexibility.

Rationale
I considered an offset scheme in which offsets are perfectly in-kind, delivering no net loss (NNL) of biodiversity.The associated ecological benefits were denoted by V (collapsing the spatial, temporal, and ecosystem type dimensions into a single number) and economic costs by C, and V and C served as measures of scheme performance.I introduced spatial temporal and type flexibility by allowing levels of out-kind restoration to increase, so that more distant sites qualified for trading and time lags between development and restoration and deviations between restored and lost biodiversity were allowed.In the scope of our work, all three types of flexibility reduce the ecological value (per hectare) of restored sites.Therefore, V declines (representing a net loss of biodiversity); although nominally (i.e., in terms of total area), NNL it is still achieved.The increased flexibility allows for cost savings, reducing C. To assess the ecological-economic trade-off of offsetting flexibility, I plotted C as a function of V for various levels of flexibility.The strength and shape of the trade-off were analyzed as functions of a number of ecological and economic parameters.

Basic land-use model
I considered a model landscape consisting of 20×20, square grid cells (land parcels).Each land parcel (i) had, without loss of generality, a size of 1 and could be used for economic purposes, such as intensive agriculture, or for conservation.Conservation of parcel i incurred a profit loss per time step, henceforth termed conservation cost (c i ).For convenience, the length of a time step was 1 year.The c i in the model landscape were normally distributed with a mean of 1 (so all cost parameters were effectively scaled with respect to that mean cost) and standard deviation σ.They were spatially autocorrelated with a correlation length l, so that "cost hills" and "cost valleys" had spatial extents of about l (Drechsler et al., 2021).The ecological values v i of the land parcels were, without loss of generality, scaled to the interval [0, 1]; thus, the highest value was set to 1 and the lowest to 0. The biodiversity values of conserved land parcels ranged from some minimum v and one, and economically used land parcels had the lowest value (0).
Initially, n 0 land parcels were conserved, each with a maximum v i of 1. Their spatial locations were sampled randomly from the entire model landscape.To explore the impact of their spatial arrangement, the conserved land parcels could be spatially aggregated.The degree of spatial aggregation was measured by α, where the larger α was, the stronger the aggregation (Appendix S1).
A conservation offset scheme makes sense only if the conserved land parcels are not the ones with the lowest costs among all land parcels; otherwise, there would be no supply or demand for conservation credits.Instead, in our analyses, the conservation costs and locations of the initially conserved land parcels were not correlated.
To model land-use change, Simpson et al. (2022), for example, considered that landowners of less profitable land may restore their land parcel to earn conservation credits that they sell to landowners who wish to develop their land.The authors established a demand and a supply function for credits whose intersection represents the equilibrium credits price, and the associated land-use pattern.The transactions in the market and the land-use change were assumed instantaneous, so effectively, their model has two periods: the initial land-use pattern and the changed land-use pattern.
I followed a similar approach by assuming an initial and a changed land-use pattern, creating again two periods.Land use in the first period was described by x i (i = 1, …, N), where x i = 1 represents conservation and x i = 0 economic use.Analogously, land use in the second period was described by y i (i = 1, …, N), where y i = 1 represents conservation and y i = 0 economic use.Each of the periods may, and in general will, consist of a number of time steps (years).
As in Simpson et al. (2022), land-use change was synchronous so all land parcels changed their land use at once (or did not change at all).In a perfect credits market (Simpson et al., 2022), the changed land-use pattern was cost-effective so that the n 0 least costly land parcels were conserved and the others were in economic use.Thus, rather than establishing supply and demand functions and searching for an equilibrium, I identified the set of the n 0 least costly land parcels to conserve them, whereas the initially conserved but not least costly land parcels were developed for economic use.All other (economically used or conserved) land parcels did not change their land use.The changed land-use pattern was thus determined by the minimization problem meaning that the sum of the costs of the newly conserved (y i = 1) land parcels is minimized (first line of the equation) under the constraint that at least n 0 land parcels are conserved (no area net loss [second line]), and each land parcel is either conserved (y i = 1) or not (y i = 0).Equation ( 1) is based on the assumption that restoration is instantaneous and costless.To introduce restoration costs and time lags, restoration incurred a cost r per year (constant and identical for all land parcels) and lasted T years (identical for all land parcels), so the restoration cost (R) of a restored land parcel was the sum of the discounted annual restoration costs (r) over the T years with annual discount rate (q) (Appendix S2, which also contains further mathematical details).

Introduction of flexibility in time
Flexibility in time was increased or decreased by awarding conservation credits at the initiation of restoration or only at the completion of restoration (lending vs. savings banks [Bekessy et al., 2010]), respectively.As outlined in the "Introduction," lending banks usually include multipliers, such that each developed hectare of formerly conserved land must be offset by m > 1 ha of restored land.As argued in Appendix S3, a landuse change involving the economic development of a conserved land parcel (i) and the restoration of an economically used land parcel (j) took place if the forgone profit associated with restoration (c j ) times the multiplier (m) was below the gained profit (c i ) of the developed land parcel.
In the savings bank (considered without multipliers), the possibility of failed restoration affected the land-use change because restored land parcels that failed did not earn any credits and effectively did not contribute to the total number of conserved (habitat) parcels.I assumed that a restoration project failed with probability φ (again, assumed identical for all land parcels).Further mathematical details are in Appendix S3.Although in practice a continuum exists between savings and lending banks, by introducing credit release schedules, I considered these two pure schemes extremes.

Introduction of flexibility in space
Spatial flexibility means there are no spatial constraints for the restoration of land parcels, whereas when this flexibility is restricted, it usually means the restored land parcel must not be too far away from the developed parcel (Yu et al., 2018;zu Ermgassen et al., 2020).To simplify, I relaxed this requirement by requiring that a restored land parcel be close enough to at least one of the initially conserved land parcels.This decision was based on the consideration that the initially conserved land parcels formed some sort of network and that it is sufficient for the restored land parcels to be close enough to the network rather than to a particular land parcel in that network.A restored (and previously economically used) land parcel i qualified for a feasible offset if there was at least one land parcel j that was conserved initially (x j = 1) and had a Euclidean distance (d ij ) to the restored land parcel below some maximum d max .This effectively excluded all land parcels farther away from any initially conserved land parcel than d max .

Introduction of flexibility in type
For flexibility in type, a region is usually considered to consist of several ecosystem types, and if offsets occur on only a hectare basis, rather than explicitly considering each ecosystem type separately, the preservation of all types cannot be guaranteed (Bull et al., 2015;Grimm, 2021).I simplified the analysis by considering only a single target type whose preservation was compromised by offsetting due to the presence of other types in the model region.Formally, I considered this by setting the ecological values (v i ) of all initially conserved land parcels (x i = 1) to 1, representing the target ecosystem type to be preserved.All other land parcels (x i = 0) had ecological values from some lower bound v to one, representing ecosystem types more or less equivalent to the targeted type.I assumed these values were random uniformly distributed numbers from the interval [ v, 1].
Full flexibility in type meant that, independent of v i , the restoration of any land parcel qualified as an offset.Flexibility was restricted by qualifying only land parcels with v i that exceeded some minimum v (v min ).(c, d) benefit obtained from biodiversity offsetting under lending (i.e., biodiversity credits awarded with the initiation of a restoration project) and savings (biodiversity credits awarded for complete and successful restoration projects) bank models (cross-hatched red, in the savings bank, restored land parcels that failed after T years switch to economic use and do not incur any cost [Drechsler, 2022]; cross-hatched green, only in the lending bank, successfully restored land parcels contribute to ecological benefit).

Economic valuation of the land-use dynamics
The total conservation cost summed over all years of the landuse dynamics depended on the offsetting scheme (lending vs. savings bank).In the lending bank, credits were awarded with the initiation of restoration projects, so land parcels could be developed and the cost-minimizing land-use pattern was reached immediately in the first model year.Initially, conserved land parcels contributed to the total conservation cost only if they were also included in the cost-minimizing set.The total conservation cost, therefore, was given by the discounted sum of the annual conservation costs of the finally conserved land parcels plus the restoration costs of the (initially economically used) restored land parcels (Figure 1a).
In the savings bank, if there was a restoration time lag, initially conserved land parcels could be developed only after the restoration projects have been completed after T years.The total conservation cost during these T years was thus determined by the conservation costs of the initially conserved land parcels plus the restoration costs of the restored land parcels.Only after those T years were the initially conserved land parcels that were not included in the cost-minimizing set developed, and only the land parcels that were conserved afterward contributed to the total conservation cost (Figure 1b).Further mathematical details are in Appendix S4.

Ecological valuation of the land-use dynamics
Land parcels conserved initially and after the land-use change had a v i of 1, and, similar to the conservation costs, their total ecological benefit was determined by summing their discounted values.In the lending bank, land parcels used economically and restored finished their restoration successfully with probability 1 -φ after T years to obtain their v i .Their total ecological benefits were discounted, summed over all years, and added to obtain the total ecological benefit for the lending bank (Figure 1c).
In the savings bank, land parcels conserved initially but developed at time T after the restoration project were completed contributed to these T years with v i = 1, and land parcels that were initially used economically and restored contributed v i ∈ [ v, 1], which were discounted and summed to be added to the ecological benefit (Figure 1d).Further mathematical details are in Appendix S5.
Two other features were included in the model.First, I considered that the connectivity of restored land parcels j-and  Annual discount rate q 0.05 0.02, 0.08 their contribution to the ecological benefit-depended on their distance d ij to the nearest initially conserved land parcel i.This was modeled by multiplying the benefits (v j ) of restored land parcels by where 1/β may be identified with the spatial interaction length for that ecosystem type (such as species dispersal distance).The second feature was motivated by the observation that even successful restoration projects do not always lead to the target ecosystem type with certainty but may have deviating ecological characteristics.To consider this uncertainty, v i was replaced by where u i is a uniform distributed random number from the interval [0, 1], such that w i has an expected value of v i and an uncertainty range of ±v i .

Model analyses
For a given combination of model parameter values, the land-use dynamics under the lending and the savings banks (separately) were simulated 10,000 times and averages of the total ecological benefit V and the total economic cost C were calculated.The ranges of the model parameters are in Table 1.Justification of their ranges is in Appendix S6.Model parameter combinations were formed by setting all parameters at their base values (base scenario) and from there varying individual parameters, 1 at a time, up and down.Which model parameters were varied depended on the chosen flexibility experiment.Six experiments were carried out to address the three types of offsetting flexibility and interactions among flexibility types.
A major focus of my analyses was the impact of model parameters and flexibility parameters on the ecological benefit and the economic cost.Two effects are trivial.First, a higher initial number of conserved land parcels n 0 implies higher benefits and costs.Thus, to allow for better comparison and reveal nontrivial effects, the values of V and C obtained for n 0 = 20 were multiplied by 2 (40/20) to be comparable with the results obtained for the base value n 0 = 40.Analogously, the values obtained for n 0 = 100 were multiplied by 0.4 (40/100).
The second trivial effect was due to the value of the discount rate (q).Assume some cost or benefit x occurs in every year.Then, the sum of the discounted x over all years from present to infinity is which equals 51x, 21x, and 13.5x for the considered discount rates of q = 0.02, 0.05, and 0.08, respectively.Therefore, a decrease in the discount rate from 0.05 to 0.02 leads to a trivial (nominal) increase in quantity X by a factor of 2.43 (51/21).
To exclude this trivial effect, benefits and costs obtained for q = 0.02 were multiplied by 0.41 (21/51) to be comparable with those obtained for the base value q = 0.05, and benefits and costs obtained for q = 0.08 were multiplied by 1.54 (21.0/13.5).

Flexibility experiments
For spatial flexibility, the d max for offsets was varied in 20 equal steps from 0 to 20, where the lower bound meant that only initially conserved land parcels were eligible for offsetting (implying no land-use change), whereas the upper bound represented a case without spatial restriction.In this experiment, parameters associated with time and ecosystem type (ecological value) had no effect and were set to φ = 0, q = 0.05, and v = 1.The restoration time lag was set to T = 5.The other parameters varied up and down from their base values, as described in the previous section.Because temporal issues were ignored, only the lending bank was considered.
For temporal flexibility and restoration failure, the lending bank, with multipliers that varied from 1 to 5, was compared with the savings bank.Spatial and type issues were ignored, so l = 0, α = 0, β = 0, and v = 1.The other parameters varied up and down from their base values.
For flexibility in ecosystem type, the v min that qualified for offsetting was varied in 20 equal steps from the smallest possible v i (unlimited flexibility) to 1 (only land parcels with exactly v i = 1 qualify for offsetting).Spatial and temporal issues were ignored, so l = 0, α = 0, β = 0, φ = 0, and q = 0.05.Similar to the first experiment, the restoration time lag was set to T = 5.The other parameters varied up and down from their base values.
For the base scenario, interactions between different dimensions of flexibility were considered by restricting one or two dimensions of flexibility and analyzing the impact of the respective third dimension on B and C (details in Appendix S7).

Spatial flexibility
Values for V and C decreased as d max increased (Figure 2a) (each cross hair on the black line represents one level of d max with the associated V and C obtained by the optimization of Equation 1 under the described constraints).The features of interest were the lengths and the slopes of the lines.A long or short line indicated the degree of d max has a strong or weak, respectively, overall impact on V and C. A large or small slope indicated that a given change in the benefit was associated with a large or small, respectively, cost change.If one considers zero flexibility with maximum V = 440 and C = 840 as the reference situation, a high slope meant that large cost savings were achieved for a given loss of benefit.A large C for given B represented a reduced level of cost-effectiveness.
As cost-variation increased (red → black → green lines in Figure 2a), impact of d max on V and C increased (line length increases) and the cost per benefit (slope of the line) increased.The reason was that at a high cost-variation, the cost difference between initially conserved and restored land parcels was high, so high cost savings were achieved by the offsetting process.In addition, a high cost-variation made restoration more profitable, so more credits were available in the market, which increased the rates of development and restoration and strongly reduced V and C under unrestricted flexibility (long green line).
Increasing restoration costs (dark blue → black → pink lines in Figure 2a) reduced the overall impact of d max .The reason was that high restoration costs reduced the profitability of restoration and thus reduced the amount of conservation credits in the market and reduced overall land-use change and decline of V and C. For zero restoration cost (dark blue line), C was, for moderate levels of flexibility, higher than for nonzero restoration cost.The reason for this was the highly nonlinear shape of the trade-off curve (Appendix S8).
A small initial number of conserved land parcels (light blue line in Figure 2a) led to a large effect of spatial flexibility on V and C (that V and C were rescaled as described in "Model Analyses").The slope of the line was independent of n 0 , so the cost per benefit did not depend on n 0 .
None of the three model parameters (cost correlation length, spatial aggregation of initially conserved land parcels, and inverse ecological interaction range) affected the impact of d max on C (Figure 2b): all the lines in Figure 2b end at about the same level of C.
The cost correlation length (red → black → green lines in Figure 2b) had only a weak effect on the impact of d max on B.
At strong spatial aggregation of initially conserved land parcels (α, pink line in Figure 2b), an increasing spatial flexibility reduced the ecological benefit more strongly than at small α.The reason was that at large α, the initially conserved land parcels were clustered, so they had fewer direct neighbors than at α = 0, for which the initially conserved land parcels were spatially dispersed (Appendix S1).Thus, at large α, rather few land parcels existed whose restoration would contribute greatly to the ecological benefit (Equation 2), and there was no reason these should have particularly low costs.Thus, increasing the spatial flexibility led to a strong shift of restoration activities toward more distant land parcels, implying a larger decline in ecological benefit.
When β = 0 (unlimited ecological interaction range), the spatial location of restored land parcels had no effect on the ecological benefit (Equation 2), so spatial flexibility had only a little adverse effect on ecological benefit (light-blue line in Figure 2b).The fact that the effect was not zero lies in the time lag T during which the number of habitat parcels was temporarily reduced.The higher the spatial flexibility, the more land parcels were profitable for restoration and the higher the rates of habitat development and restoration, which increased the temporary reduction of habitat parcels.Conversely, large β represented a strong dependence of B on the spatial arrangement of the restored land parcels, so spatial flexibility quite strongly reduced the ecological benefit.

Temporal flexibility
The effect of the multipliers on B and C was highest for large cost-variation σ, large initial number of conserved land parcels n 0 , and zero restoration cost r = 0 (Figure 3a).For sufficiently large multipliers, the ecological benefit increased beyond the reference value of 840.Except for r = 0, all lines had a similar shape, which is not relevant in the analysis of temporal flexibility.Instead, I was interested in the locations of the circles, showing the performance of the savings bank, relative to the corresponding lines.Starting with the base scenario (black color), the savings bank delivered the same level of B at a slightly higher C (i.e., was slightly less cost-effective, than the lending bank).(The main reason for the consideration of a range of multipliers was to hit a value of B equal to the one generated by the savings bank, allowing for this type of comparison.)Whether the savings bank incurred a higher cost than the lending bank depended, of course, on the chosen model parameter values in the base scenario and was not generalizable.Instead, it served as a reference for the assessment of the effects of the model parameters.
With increasing conservation cost-variation (red → blackgreen color in Figure 3a), the cost difference between savings and lending banks (i.e., the level of cost-effectiveness of the lending bank relative to that of the savings bank) increased.The reason is that, similar to the spatial flexibility, at high cost-variation, the offsetting process generated high cost savings.Because the lending bank allowed for more flexibility, its cost-effectiveness advantage increased.
At zero restoration cost (r = 0, dark blue line in Figure 3a), the savings bank was more cost-effective than the lending bank, whereas at r = 0.2 (pink line in Figure 3a), the opposite was observed.One might have expected that for zero restoration cost, the lending bank would be more cost-effective than the savings bank because under zero restoration, cost habitat restoration is profitable, which allows for substantial reallocations of conservation efforts from high-cost to low-cost land parcels.However, in the presence of restoration failure (as is assumed with φ = 0.4), the lending bank achieved the same ecological benefit as the savings bank only with rather high multipliers.These in turn rendered habitat restoration in the lending bank unattractive, so effectively, there was less reallocation from high-cost to low-cost land parcels, and altogether in the savings bank, the same ecological benefit was achieved at lower costs than in the lending bank.
An increasing initial number of conserved land parcels (light blue → black → gray color in Figure 3a) raised the economic cost in the savings bank more than in the lending bank.The reason is that a large (initial) number of conserved land parcels involved high amounts of developed and restored land parcels, which is better enabled by the lending bank.
An increasing restoration time lag (T, red → black → green color in Figure 3b) reduced the cost-effectiveness of the savings bank (cost C for given benefit B) relative to that of the lending bank.For both scheme types, an increasing T raised the cost.In the lending bank, the reason for the cost increase was that higher multipliers were needed to obtain the same ecological benefit, whereas for the savings bank, the reason for the cost increase was that during the restoration time, conservation efforts were not allocated to the least costly land parcels.The latter factor appeared to count more strongly than the former, such that the cost in the savings bank increased more as T increased than it did in the lending bank.
A high risk of restoration failure (pink color in Figure 3b) greatly increased C in the savings bank because few credits became available to develop habitat and allocate conservation efforts to less costly land parcels.The cost in the lending bank also increased but less strongly than in the savings bank, so altogether, the cost-effectiveness of the lending bank increased at high risk of restoration failure.
An increasing discount rate (light blue → black → gray color in Figure 3b) slightly increased the cost in the lending bank and moderately increased the cost in the savings bank.The reason was that the costs in the savings bank were incurred in the near term, which was most strongly weighted by high discount rates.Therefore, an increasing discount rate increased the costeffectiveness of the lending bank relative to that of the savings bank.

Flexibility in type
The results for the influence of the model parameters costvariation, annual restoration cost, and initial number of habitat parcels on the impact of type flexibility were very similar to those shown in Figure 2a, and the explanations are the same.An increase in the lower bound of the ecological benefits (green → black → red lines) not unexpectedly increased the overall influence of type flexibility (Figure 4b) (length of the lines) and reduced the ecological benefit B (lines shift to the right).

Interactions between flexibility dimensions
A restriction of any dimension of flexibility reduced the overall impact (length of the trade-off lines) of the other dimensions, reduced the scheme cost-effectiveness (trade-off lines shift upward) or both.(Detailed results in Appendix S7).

DISCUSSION
When the spatial distribution of the conservation costs (forgone economic profits) and the spatial distribution of conserved land parcels of conservation offsets match perfectly, such that the least profitable (i.e., least costly) sites are conserved, there is no reason for profit-maximizing landowners to change their land use.However, if-due to environmental or economic changethere is a mismatch, such that economically profitable sites are under conservation and unprofitable sites are used economically, there will be supply and demand for conservation credits, associated with turnover between conserved and economically used sites.The results of my model analyses of the impacts of spatial, temporal, and ecosystem-type offset flexibility showed that increasing offset flexibility reduced economic costs and ecological benefits.
The trade-off lines in Figures 2-4 between economic cost and ecological benefit reveal several insights.A large horizontal extension indicates that the ecological benefit was very sensitive to the degree of flexibility.This was found for large cost-variation, low restoration costs, and small initial number of conserved land parcels.At large cost-variation, the force of the market to shift conservation efforts to the least costly sites was strongest.Small restoration costs resulted in a large supply of conservation credits, which drew conservation efforts to ecologically less valuable sites unless flexibility was restricted.
Spatial flexibility led to the largest decline when the range of ecological interaction was small (β in Table 1 large), and ecosystem type flexibility led to the strongest decline when variation in the local ecological benefits of the land parcels was large ( v in Table 1 small).Multipliers that were too small in the lending bank led to the strongest declines in the ecological benefit when the time lag between initiation and completion of restoration was small or the risk of restoration failure was large.The latter effect was self-evident, whereas the former effect was because-similar to a small restoration cost-a small time lag induced high trading activity, which reduced the ecological benefit.
The second characteristic of the trade-off lines is their steepness; large positive slopes indicated high cost savings for a given loss in ecological benefit.This was found for large cost-variation and long-ranged ecological interaction (small β).The effect of the restoration cost was ambiguous, but generally, increasing restoration cost increased the cost savings for a given loss of ecological benefit (Appendix S8).At large cost-variation, the cost-effective allocation of conservation measures was strongly determined by the cost distribution (Naidoo et al., 2006), and an increased flexibility allowed for particularly high cost savings.Long ecological interaction range allowed for spatial flexibility and associated cost savings without much loss of ecological benefit.
The savings and lending banks compared in "Temporal Flexibility" represented low and high levels of temporal flexibility, respectively.The results of the comparison should not be interpreted as arguments in favor of one or the other scheme, but as an indication under which conditions some increase of temporal  1]; crosses, for the base scenario, the values obtained for the 21 levels of v min ).
flexibility may be worth considering.An increasing restoration cost and increasing restoration time lag reduced the lending bank's cost of delivering a given level of ecological benefit relative to that of the savings bank because (similar to the arguments above) they slowed trading activity, so smaller multipliers were required to ensure the same ecological benefit as that of the savings bank.The effect of the restoration time lag was not consistent with Drechsler's (2022) findings, perhaps because in Drechsler (2022), the conservation costs changed continuously over time rather than synchronously between two periods.
An increasing risk of restoration failure reduced the lending bank's cost of delivering a given level of ecological benefit relative to that of the savings bank because it overly diminished market activity in the savings bank and induced high economic costs, which appeared to be larger than the costs associated with the (appropriately set) multipliers in the lending bank.This is consistent with Drechsler's (2022) findings that an increasing restoration risk increases the cost-effectiveness of the lending bank relative to that of the savings bank.A high restoration risk implies in the savings bank a low supply of credits, so costly conserved land parcels cannot be developed and must stay in conservation.While in the lending bank a high restoration risk is mitigated by a sufficiently high multiplier (m), implying that the restoration failure of a particular land parcel is accepted if a sufficiently high number of other restoration projects is initiated.Effectively, the risk associated with the restoration of a single land parcel in the savings bank is in the lending bank spread over m restoration projects.An increase in the restoration risk thus increased the costs of both schemes, but it did so more strongly in the savings bank than in the lending bank (Figure 3b).
In the model, flexibility always reduced the ecological benefit because spatial distance between development and restoration was penalized, and restored land parcels could never have a higher ecological value than developed parcels; and a time lag between development and restoration led to a penalized temporary loss of biodiversity.This provides a rather pessimistic view of the value of restored sites (somewhat consistent with, e.g., with Bull et al., 2015 andzu Ermgassen et al., 2020]), ignoring potentially positive outcomes of restoration ("trading up" [Bull et al., 2015;Habib et al., 2013]).The only option to achieve net gain in our model is through sufficiently large multipliers (Figure 3).Additionally, a restriction on flexibility in one dimension reduced the overall impact of the other dimensions.
Although a comparison of specific results with the literature is impossible due to differences in the considered modeling purposes and model structures, some general statements can be made.First, in line with Bull et al. (2015), Habib et al. (2013), and Giannichi et al. (2019), flexibility can have substantial impacts on ecological benefit (biodiversity) and economic costs, and it is important to distinguish between the different dimensions of flexibility because their ecological and economic impacts depend on the specific ecological and economic conditions.
In the lending bank, the ecological benefit of the savings bank could be matched only with appropriate multipliers, which agrees with zu Ermgassen et al.'s (2019) findings that restoration failure can, with acceptable certainty, be offset only by appropriate multipliers.In agreement with Bull et al. (2017), multipliers also played a central role in the achievement of net biodiversity gain.
Compared with previous studies on flexibility, my analyses emphasize the importance of the costs (forgone economic profits) incurred by restoration measures and their (spatial) distribution.If the costs are very heterogeneous, they can decisively affect the cost-effective allocation of conservation measures (Naidoo et al., 2006) and thus also affect the optimal degree of flexibility of conservation offsets.The credits price in a market is not only a signal of ecological value and scarcity (zu Ermgassen et al., 2020, section 6), but also of the economic cost of conservation.
My analyses were based on a number of assumptions.First, beyond the mismatch between conservation costs and conservation efforts that may be regarded as the result of a past change in the conservation costs, no further exogenous change of the ecological and economic conditions (as, e.g., by Drechsler, 2022) was considered.Similarly, restoration failures occurred during the restoration process but not later in the future.The latter would reduce ecological benefits, especially at high restoration rates that are favored by high levels of flexibility.Possible correlations between ecological value and conservation cost were ignored.Positive and negative correlations would aggravate or alleviate, respectively, the flexibility trade-offs.A positive correlation could occur if within the mitigation hierarchy many low-cost avoidance and mitigation measures were exhausted and only costly sites with sufficiently large (potential) ecological value remain for restoration.
Second, the issue of ecosystem type was considered rather simplistically (compared, e.g., with Bull et al., 2015).A simplification on the ecological side was that only habitats were considered, disregarding the dynamics of biodiversity in those habitats.On the economic side, other costs, aside from restoration costs and forgone profits, such as transaction costs and monitoring and enforcement costs, were ignored.Furthermore, landowners were assumed to decide perfectly rationally and did not behave strategically and market failure (Wissel & Wätzold, 2010;zu Ermgassen et al., 2020) was ignored.In the sensitivity analysis, varying model parameters 1 by 1 precluded the detection of interactions between model parameters.
Finally, broader issues around conservation offsets, such as additionality (Giannichi et al., 2019;zu Ermgassen et al., 2020) and inappropriate baselines (Simmonds et al., 2019), were not considered explicitly.However, their effects may be similar to those of an increased type flexibility and risk of restoration failure.In my model, increased type flexibility was considered by qualifying restoration sites that had a lower local ecological benefit than the developed site, and the risk of restoration failure may include the risk that the ecological value of the restored site is measured against an inappropriate baseline that overestimates the local biodiversity gain.
To conclude, the impacts of flexibility on the ecological benefits and economic costs of conservation offsets strongly depended on the ecological and economic conditions.Level of flexibility may be related to the position of the policy on the mitigation and conservation hierarchy, such that at the top of the hierarchy (avoid), flexibility is low, whereas at the bottom (offset), it is high.
The results of my model analyses indicated that a trade-off exists between the ecological and economic impacts of flexibility and between the objective of minimizing biodiversity loss and the objective of cost-effectiveness (by minimizing biodiversity loss at least cost).For instance, at high cost-variation, the ecological benefit strongly declined as flexibility increased, calling for small levels of flexibility to avoid large biodiversity losses.This limitation of flexibility, however, forfeits the substantial cost savings that can be obtained from flexibility, especially at high cost-variation, which reduces the cost-effectiveness of the scheme.Similarly, the savings bank delivered NNL of biodiversity with higher certainty than the lending bank, but it can be less cost-effective in the sense that a given level of ecological benefit can be achieved only at higher economic costs.It is a political decision to prioritize these two objectives of ecological effectiveness and cost-effectiveness, as well as other societal objectives, such as equity and acceptance.
Finally, although the model results point to some ecological and economic consequences of flexibility, and by this may enrich the discussion about offset scheme design, the highly stylized nature of the model precludes literal implementation of the results.

FIGURE 1
FIGURE 1 (a, b) Cost incurred and (c, d) benefit obtained from biodiversity offsetting under lending (i.e., biodiversity credits awarded with the initiation of a restoration project) and savings (biodiversity credits awarded for complete and successful restoration projects) bank models (cross-hatched red, in the savings bank, restored land parcels that failed after T years switch to economic use and do not incur any cost[Drechsler, 2022]; cross-hatched green, only in the lending bank, successfully restored land parcels contribute to ecological benefit).

FIGURE 2
FIGURE 2 Economic cost of conservation offsetting versus ecological benefit as spatial flexibility increases from upper right (d max = 0) to lower left (d max = 20) (colors, six model parameters varied relative to their values in the base scenario [Table1]; crosses, for the base scenario, the values obtained for the 21 levels of d max ).

FIGURE 3
FIGURE 3 Economic cost versus ecological benefit of conservation offsetting under the lending bank model (described in "Flexibility in Type") as the multiplier increases from left (m = 1) to right (m = 5) (colors, six model parameters varied relative to their values in the base scenario [Table1]; circles, corresponding values for the savings bank [see "Flexibility in Type"]; crosses, for the base scenario, the values obtained for the 21 levels of m).

FIGURE 4
FIGURE 4 Economic cost versus ecological benefit of conservation offsetting as type flexibility increases from upper right (v min = 1) to lower left (v min = 0) (colors, four model parameters varied relative to their values in the base scenario [Table1]; crosses, for the base scenario, the values obtained for the 21 levels of v min ).

TABLE 1
Ranges of parameter values considered in the model analyses of flexibility trade-offs in conservation offsets.